Curve Equation Research Articles

Nitrogen-Doped Carbon Dots Enhanced Hydrogen Carbonate-Hydrogen Peroxide Chemiluminescent Reaction and its Application in Ascorbic Acid Sensing.

Nitrogen-doped carbon dots (N-CDs) were prepared by self-exothermic procedure using grasshopper powder as a single precursor. The prepared N-CDs not only have excellent fluorescence properties, but also can catalyze and enhance the ultra-weak chemiluminescence of NaHCO3-H2O2. The reaction conditions of NaHCO3-H2O2-N-CDs CL were optimized. Under the optimal experimental conditions, when AA was added to the NaHCO3-H2O2-N-CDs CL system, AA had a significant inhibitory effect on the CL intensity of NaHCO3-H2O2-N-CDs. There was a good linear relationship between the calculated lg(I0/I) and the concentration of AA (C), and the calibration curve equation was lg(I0/I) = 0.03667C-0.00708 (µM). The established CL analysis method has a detection limit of 0.12 µM for AA and a linear range of 0-50 µM. The selectivity of CL method was evaluated, and the method was successfully applied to the determination of AA in vegetable and fruit samples. The spiked recoveries were between 88.9% and 118.9%, which indicated that the method was simple, rapid, and sensitive, and had great potential in the determination of AA in foods.

Self-disgust mediates the effect of problematic mobile social media use on non-suicidal self-injury in adolescents: A latent growth curve analysis.

Previous research linked problematic mobile social media use to non-suicidal self-injury (NSSI). However, little research explored the underlying mechanism. Drawing on the social displacement hypothesis, which suggests that excessive social media use may disrupt offline social interactions, leading to negative emotional experiences, the study employs a longitudinal design to explore the relationship between problematic mobile social media use and NSSI, with a specific emphasis on the mediating role of self-disgust. A total of 1,684 Chinese adolescents (52.3% females; Mage = 14.59 years, SDage = 1.27) completed self-report questionnaires regarding problematic mobile social media use, self-disgust, and NSSI. The assessment was conducted in three waves, 6 months apart. Using latent growth curve and structural equation modeling, our study observed a consistent linear decline in NSSI levels over time. Higher initial NSSI levels correlated with a slower reduction. Problematic mobile social media use positively influenced the initial level of NSSI. Additionally, self-disgust played a mediating role in the relationship between problematic mobile social media use and NSSI. The study underscores the importance of understanding the emotional experiences behind social media use, beyond mere usage duration. By revealing the mediating role of self-disgust, it provides new insights into the complex interplay between problematic mobile social media use and adolescent NSSI.

A novel harmonic drive with the full conjugate tooth profile

This paper presents an approach for designing a novel tooth profile of harmonic drives, which is composed of two pieces of curves, hypocycloid and epicycloid, generated by the rolling circles with appropriate radii. Compared with the conventional double-circular-arc or cycloidal tooth profile of harmonic drives, the tooth profile is characterized by full conjugation, more number of engaged teeth, and can be expressed analytically, etc. Firstly, the generation of the cycloids are briefly described, and then their conjugate criterion is investigated systematically based on Camus’s theorem. Secondly, the tooth profile equations for the circular spline and flexspline are established and the deformed neutral curve equation is derived. Next, the contact properties among the tooth profiles, including the line of action, meshing angle, etc., are studied systematically. Finally, a finite element model and a physical prototype for the harmonic drive with the tooth profile are developed, respectively. The effectiveness of the design method is verified by the contact performances simulation. The research may provide a new thought for the innovative design of harmonic drives with full conjugate tooth profile.

Effect of annealing on the corrosion-fatigue strength and hot salt corrosion resistance of fine-grained titanium near-α alloy Ti-5Al-2V obtained using Rotary Swaging

The corrosion-fatigue strength in 3 % aqueous NaCl solution and the resistance against hot salt corrosion (HSC) of the fine-grained near-α alloy Ti-5Al-2V (Russian analogue of Grade 9 titanium alloy with increased aluminium content) have been studied. The properties of the Ti-5Al-2V alloy in the coarse-grained state, in the fine-grained state after cold Rotary Swaging (RS), in the partly recrystallized state and in the fully recrystallized state have been investigated. The mechanical properties of the alloy were characterised using compression tests and microhardness measurements. The effects of RS, the annealing temperature, the time on the characteristics of corrosion destruction of the surface and the composition of the products of the HSC were studied. RS was shown to increase the depth of the intergranular corrosion defects, whereas recrystallization annealing promoted an increase in the corrosion resistance of the Ti-5Al-2V titanium alloy. The parameters of the Basquin equation for the corrosion-fatigue curves for the near-α Ti-5Al-2V alloy in the coarse-grained state, in the severely strained state and after recrystallization annealing were determined for the first time. An effect of non-monotonous dependencies of the slopes of the corrosion-fatigue curves for the strained near-α Ti-5Al-2V alloy on the recrystallization annealing temperature has been observed.

A novel magnetoelastic biosensor consisting of carbon quantum dots/nitrocellulose membranes and NiFe2O4/ polylactic acid based on 3D printing for α2-macroglobulin detection

α2-macroglobulin (α2-M) have crucial clinical significance as a potent biomarker for diabetes nephropathy (DN). There is an increasing demand for rapid detection of α2-M. Herein, a magnetoelastic (ME) biosensor with a layered composite structure is developed for α2-M detection. Based on 3D printing, the basal layer of the biosensor is prepared as a grid structure fabricated by polylactic acid (PLA) doped with NiFe2O4. The conductivity of the biosensor was improved significantly due to the addition of multi-walled carbon nanotubes (MWCNTs). The biological site for capturing α2-M antigen was provided by the carbon quantum dots (CDs) coupled with anti-α-2M (anti-α2-M@CDs) in the nitrocellulose filter (NC) membrane. Meanwhile, the distribution of antibodies on the biosensor surface can be observed more directly due to the fluorescence characteristics of CDs. The biosensor in this work can realize multi-pattern recognition of fluorescent signal and electromagnetic signal. The results show that the limit of detection (LOD) was 0.506 ng/mL in the linear range from 10 ng/mL to 100 µg/mL and the linear equation of fitting curve is: y = 0.21 x - 0.15. The ME biosensors with a simple preparation method have advantages of high sensitivity, good stability and low LOD, showing the great potential for α2-M detection.

Erroneous Applications of Fractional Calculus: The Catenary as a Prototype

In this work, we study the equation of the catenary curve in the context of the Caputo derivative. We solve this equation and compare the solution with real physical models. From the experiments, we find that the best approximation is achieved in the classical case. Therefore, introducing a fractional parameter arbitrarily can be detrimental. However, we observe that, when adding a certain weight to the chain, fractional calculus produces better results than classical calculus for modeling the minimum height.

The use of thermal performance analysis to improve conservation management: The case of the invasive Red Sea swimming blue crab Portunus segnis

The latest report from the Intergovernmental Platform on Biodiversity and Ecosystem Services (IPBES) expresses concern over the global proliferation of non-native species (NIS) driven by increasing temperatures. In 2023, the invasive blue crab Portunus segnis in the Mediterranean experienced a significant range expansion due to warmer waters in northern and western regions. Recognizing thermal tolerance as crucial for conservation, this study, using the blue crab as a model, emphasized the importance of considering thermal metabolic performance in conservation efforts. In this study, we experimentally measured the metabolic performance of P. segnis at different temperatures (from 7 to 42°C) using an oxygen consumption measurement system. The thermal performance curve (TPC) of P. segnis rose from 0.016 ± 0.011 mgO2 h−1 gWW−1 (12°C) to 0.238 ± 0.011 mgO2 h−1 gWW−1 (34°C), and decreased beyond. Organisms succumbed at 7°C and 42°C. The TPC obtained was compared with 24 TPC models and the O’Neill regression was the best fitting model determining the minimum critical thresholds (CTmin) at 11.33°C and CTmax at 41.13°C. Using the TPC curve equation, we applied the curve to satellite Mediterranean temperature data for the year 2022 and for the future (RCP 4.5 and 8.5) to determine the current and future monthly distribution of favorable thermal habitats for P. segnis. Results anticipated the future expansion of the species along the Spanish, French, Italian, and Greek coasts of the Aegean Sea, providing maps to prioritize high-risk invasion areas. Additionally, in the areas where the species in currently present, results predicted a long-term persistence of the species. Understanding species' responses to temperature changes appears crucial for anticipating and addressing the impending expansion of invasive species, underscoring the urgency of nature conservation measures.

The Implicit Equation of a Holditch Curve

Holditch’s theorem is a classical geometrical result on the areas of a given closed curve and another one, its Holditch curve, which is constructed as the locus of a fixed point dividing a chord of constant length that moves with its endpoints over the given curve and that returns back to its original position after some full revolution. Holditch curves have already been studied from the parametric point of view, although numerical methods and approximations are often necessary for their computation. In this paper, implicit equations of Holditch curves of algebraic curves are studied. The implicit equations can be simply found from the computation of a resultant of two polynomials. With the same techniques, Holditch curves of two initial algebraic curves are also considered. Moreover, the use of implicit equations allows to find new and explicit parameterizations of non-trivial Holditch curves, such as in the case of having an ellipse as an initial curve.

The structural strain method for fatigue evaluation of welded components: Analytical treatment of reversed plasticity

The traction structural stress method has been adopted by various industry sectors, in addition to ASME Boiler and Pressure Code (B&PV), for fatigue life evaluation and assessment of welded components, especially for high-cycle fatigue applications. Its effectiveness has been validated and demonstrated by showing good data correlation in the form of the master S–N curve scatter band. For low cycle fatigue with the involvement of elastic-plastic deformation, the structural strain method has been recently developed by simply extending the current elastic-deformation-based structural stress method to more general elastic-plastic deformation. Closed-form structural strain solutions for elastic-perfectly plastic materials and numerical solutions for nonlinear strain hardening materials have been obtained under simple load-controlled loading and unloading cycling conditions. In this paper, the equations of nonlinear cyclic structural stress-strain curves under fully-reversed fatigue loading are analytically derived for the first time with a 3-bar model, which consists of three elastic-perfectly plastic bars. The general trends and patterns of the loading paths of the constructed cyclic structural stress-strain curves with the 3-bar model are validated with finite element analysis (FEA). Based on the insights gained from the 3-bar model and the FEA results, a simple procedure for constructing cyclic structural stress-strain curves from their corresponding monotonic loading curves are developed for both elastic-perfectly plastic model and the modified Ramberg-Osgood nonlinear strain hardening model. The effectiveness of this procedure is demonstrated by correlating low-cycle fatigue data of welded structures under pulsating and fully-reversed loading conditions.

Combined axial load-biaxial bending interaction method for L-shaped CFSP shear walls

This paper reports the development of axial load and biaxial bending interaction method for L-shaped concrete-filled steel plate (CFSP) composite shear walls based on fiber section analysis model using the uniaxial constitutive relationship of materials. Owing to the complex interaction between the two perpendicular wall limbs (web and flange) of an L-shaped shear wall, the contour shape of the My-Mz curve is asymmetric. Linear transformation was employed to reduce the asymmetry of the contour shape, eliminate the influence of dimension, and perform parametric analysis. The analysis results indicate that when 0° ≤ θ(neutral axis angle) ≤ 90°, the influence of width-to-thickness ratio (hw1/bw) and shape coefficient (γ) on the coefficient that controls the contour shape (α) was negligible. The effect of shape coefficient (γ), steel content ratio (ρ), compressive strength of unconfined concrete (fc0), and yield strength of steel plate (fyp) on α is not significant for −180° ≤ θ ≤ −90°. Further, simplified equations were suggested to determine α. The axial load-moment interaction curve expressions for distinctive loading directions were determined by establishing the calculation method for the curve's characteristic points (axial load capacity, bending capacity, boundary points). Subsequently, the characteristic points were combined with the contour shape of the axial load-moment interaction curve derived by fitting the finite element simulation data to generate the axial load-moment interaction curve equations. A design approach was finally formulated based on the equations for the biaxial moment capacity curve and the axial load-moment interaction curves of the characteristic loading directions.

Galois subcovers of the Hermitian curve in characteristic p with respect to subgroups of order p2

A (projective, geometrically irreducible, non-singular) curve X defined over a finite field Fq2 is maximal if the number Nq2 of its Fq2-rational points attains the Hasse-Weil upper bound, that is Nq2=q2+2gq+1 where g is the genus of X. An important question, also motivated by applications to algebraic-geometry codes, is to find explicit equations for maximal curves. For a few curves which are Galois covered of the Hermitian curve, this has been done so far ad hoc, in particular in the cases where the Galois group has prime order. In this paper we obtain explicit equations of all Galois covers of the Hermitian curve with Galois group of order p2 where p is the characteristic of Fq2. Doing so we also determine the Fq2-isomorphism classes of such curves and describe their full Fq2-automorphism groups.

Mechanical properties of recycled aggregate concrete containing brick particles

To investigate the mechanical properties of recycled aggregate concrete containing brick particles (RACB), compressive strength tests were conducted on RACBs with different water/cement ratios and recycled fine aggregate substitution rates. The changes in compressive strength, elastic modulus and peak strain of RACB were analysed as a function of the proportion of substituted recycled fine aggregate, and a stress–strain equation was established. A damage model was established using ultrasonic non-destructive testing technology to reveal the damage mechanism of RACB. Results show that the basic mechanical properties of RACB are best when the replacement proportion of recycled fine aggregate (r) is 30%. The model parameter a of the stress–strain curve equation is consistent with the change of elastic modulus with r. The model parameter b has a quadratic function relationship with r, reflecting the brittleness of RACB. The initial damage of RACB is relatively large, and cracks penetrate the recycled coarse aggregate, leading to specimen failure.

Modelling thermal reaction norms for development and viability in Drosophila suzukii under constant, fluctuating and field conditions

Phenological models for insect pests often rely on knowledge of thermal reaction norms. These may differ in shape depending on developmental thermal conditions (e.g. constant vs. fluctuating) and other factors such as life-stages. Here, we conducted an extensive comparative study of the thermal reaction norms for development and viability in the invasive fly, Drosophila suzukii, under constant and fluctuating thermal regimes. Flies, were submitted to 15 different constant temperatures (CT) ranging from 8 to 35 °C. We compared responses under CT with patterns observed under 15 different fluctuating temperature (FT) regimes. We tested several equations for thermal performance curves and compared various models to obtain thermal limits and degree-day estimations. To validate the model's predictions, the phenology was monitored in two artificial field-like conditions and two natural conditions in outdoor cages during spring and winter. Thermal reaction norm for viability from egg to pupa was broader than that from egg to adult. FT conditions yielded a broader thermal breadth for viability than CT, with a performance extended towards the colder side, consistent with our field observations in winter. Models resulting from both CT and FT conditions made accurate predictions of degree-day as long as the temperature remained within the linear part of the developmental rate curve. Under cold artificial and natural winter conditions, a model based on FT data made more accurate predictions. Model based on CT failed to predict adult's emergence in winter. We also document the first record of development and adult emergence throughout winter in D. suzukii. Population dynamics models in D. suzukii are all based on summer phenotype and CT. Accounting for variations between seasonal phenotypes, stages, and thermal conditions (CT vs. FT) could improve the predictive power of the models.

Determination of glucose oxidase activity by tyrosine fluorescence spectrophotometry

A novel Fe2+/Tyr/H2O2 fluorescence reaction system has been established for the purpose of analyzing glucose oxidase activity. This system involves the catalysis of glucose oxidase on glucose to produce H2O2, which in turn oxidizes tyrosine to a highly fluorescent substance under the catalysis of Fe2+. The fluorescence intensity is subsequently employed to ascertain the enzymatic activity of glucose oxidase. The enzymatic oxidation reaction and tyrosine fluorescence reaction conditions were optimized based on the H2O2 standard curve equation. Direct fluorescence spectrophotometry was used to determine the activity range and detection limit of glucose oxidase, which were found to be 7.00 × 10−5–7.00 × 10−2 U/mL and 3.36 × 10−5 U/mL (Enzyme-like activity is 6.72 × 10−4 U/mL, The enzyme reaction time is 5 min), respectively, with a relative standard deviation of less than 3.2 %. This method has been successfully applied to determine the activity of glucose oxidase in food additives, with a recovery rate ranging from 96.00 % to 102.0 %.

Monte Carlo simulation of the effect of melanin concentration on light-tissue interactions for transmittance pulse oximetry measurement.

Questions about the accuracy of pulse oximeters in measuring arterial oxygen saturation ( ) in individuals with darker skin pigmentation have resurfaced since the COVID-19 pandemic. This requires investigation to improve patient safety, clinical decision making, and research. We aim to use computational modeling to identify the potential causes of inaccuracy in measurement in individuals with dark skin and suggest practical solutions to minimize bias. An in silico model of the human finger was developed to explore how changing melanin concentration and arterial oxygen saturation ( ) affect pulse oximeter calibration algorithms using the Monte Carlo (MC) technique. The model generates calibration curves for Fitzpatrick skin types I, IV, and VI and an range between 70% and 100% in transmittance mode. was derived by inputting the computed ratio of ratios for light and dark skin into a widely used calibration algorithm equation to calculate bias ( ). These were validated against an experimental study to suggest the validity of the Monte Carlo model. Further work included applying different multiplication factors to adjust the moderate and dark skin calibration curves relative to light skin. Moderate and dark skin calibration curve equations were different from light skin, suggesting that a single algorithm may not be suitable for all skin types due to the varying behavior of light in different epidermal melanin concentrations, especially at 660nm. The ratio between the mean bias in White and Black subjects in the cohort study was 6.6 and 5.47 for light and dark skin, respectively, from the Monte Carlo model. A linear multiplication factor of 1.23 and exponential factor of 1.8 were applied to moderate and dark skin calibration curves, resulting in similar alignment. This study underpins the careful re-assessment of pulse oximeter designs to minimize bias in measurements across diverse populations.

Failing to Hash Into Supersingular Isogeny Graphs

Abstract An important open problem in supersingular isogeny-based cryptography is to produce, without a trusted authority, concrete examples of ‘hard supersingular curves’ that is equations for supersingular curves for which computing the endomorphism ring is as difficult as it is for random supersingular curves. A related open problem is to produce a hash function to the vertices of the supersingular $\ell $-isogeny graph, which does not reveal the endomorphism ring, or a path to a curve of known endomorphism ring. Such a hash function would open up interesting cryptographic applications. In this paper, we document a number of (thus far) failed attempts to solve this problem, in the hope that we may spur further research, and shed light on the challenges and obstacles to this endeavour. The mathematical approaches contained in this article include: (i) iterative root-finding for the supersingular polynomial; (ii) gcd’s of specialized modular polynomials; (iii) using division polynomials to create small systems of equations; (iv) taking random walks in the isogeny graph of abelian surfaces, and applying Kummer surfaces and (v) using quantum random walks.

Analysis of the impact of uneven permeability of surrounding rock caused by the coupling effect of ground stresses and fault structure on sudden water inrush in tunnels

Affected by fault structure and in situ stress, the heterogeneity of the permeability of surrounding rock is universal. Treating it as a fixed value will reduce the prediction accuracy of water inflow and structural head. In view of this problem, considering the coupling effect of ground stress and fault structure, the permeability of surrounding rock is regarded as a spatially discrete type, a plane one-dimensional seepage calculation model in the vertical section is constructed, and the phreatic surface drop curve equation is established. Using Taylor's formula and series expansion theorem, the equation can be reduced to the expression of the falling curve when the permeability of the surrounding rock is homogeneous. Based on Darcy's law and the law of conservation of fluid mass, the calculation formula for tunnel water inflow and external water pressure of the structure was derived and verified through ongoing construction projects. Research shows that the calculation error of water inflow can be reduced from 23.1% to 7.5% when considering the influence of ground stress and fault structure on the permeability of surrounding rock, and the calculation error of water head borne by the supporting structure can be reduced from 43.8% to 30%, which improves the prediction accuracy. Thematic collection: This article is part of the Climate change and resilience in Engineering Geology and Hydrogeology collection available at: https://www.lyellcollection.org/topic/collections/climate-change-and-resilience-in-engineering-geology-and-hydrogeology

Predicting pump-turbine characteristic curves by theoretical models based on runner geometry parameters

The characteristic curve of a pump-turbine is the essential data for calculating the hydraulic transient processes of a pumped storage power station. However, this curve is often unavailable during the preliminary design stage of pumped storage power stations. The shape of the characteristic curve directly influences the transient guarantee parameters. To date, adjusting the runner geometry to control the characteristic curve's shape for improving hydraulic transients remains a challenging issue. This paper proposes a model for predicting the characteristic curve that correlates its shape with the runner's geometric parameters. Considering the bidirectional flow in pump-turbines, two sets of governing equations are derived separately for the centripetal and centrifugal flow conditions. The governing equations for the unit discharge curve and the unit torque curve are constructed based on the energy equation and torque equation, respectively. Each term in these equations is subsequently organized into the expressions involving the runner's geometric parameters and unit parameters. To make the equations solvable, several sets of feature points are introduced. Based on the approach to obtain the feature points, an experiment/CFD (Computational Fluid Dynamics)-based prediction method and a statistics-based prediction method are proposed. Verifications using manufacturer-measured curves show that the experiment/CFD-based method is well-suited for model test acceleration and characteristic curve repair due to its higher prediction accuracy and availability, while the statistics-based method is more suitable for borrowing similar curve data during the power plant's preliminary design phase or rapidly predicting the corresponding characteristic curves during runner design. This work establishes a theoretical basis for improving hydraulic transient guarantee parameters by runner design optimization.

Research on the widths of protective coal pillars in main roadway based on the damaged foundation beam model

Long-term stability of the protective coal pillars in coal mines can ensure normal and safe use of roadways; in turn, the integrity of the roadway plays an important role in safe and efficient mining in coal mines. The initial damage and rheological damage caused by coal-seam excavation disturbance have important influences on the selection of reasonable widths of the protective coal pillars. Based on damage mechanics and the theory of elastic foundation beams, a coupled damage constitutive relationship of rock-like materials is proposed in this work by considering the influence of threshold and residual strength to establish the mechanical model of the elastic damage foundation beam. By theoretical analysis and numerical calculation, the differential equation of the deflection curve of the beam is solved, the influence range of the advance abutment pressure under the condition of coupling damage is obtained, and the width of the protective coal pillar is determined. The results show that compared with the elastic foundation beam model, after considering the coupling damage of coal, the influence range of the advance abutment pressure increases with time over a certain duration. At the end of this duration, the influence range of the advance abutment pressure remains almost unchanged. For the case considered in this paper, the long-term stability of the roadway is guaranteed when the width of the coal pillar is 120 m. The potential interference or change related to the specific situation of the site can be studied by changing the relevant parameters in the model to study different working conditions, or the damage of the roof rock beam during the mining process of the working face can be considered, which will be the subject of further research in the future.

Isolation, Characterization, and Degradation Efficiency Testing of a Paclobutrazol-degrading Bacterium: Deinococcus arenae

Objective: This study aimed to isolate and characterize a bacterium capable of degrading the pesticide paclobutrazol. The strain was obtained from soil enriched with paclobutrazol, and its degradation ability was assessed using gas chromatography (GC). Methods: A single strain was isolated from the soil solution of Ophiopogon japonicus, a plant exposed to excessive paclobutrazol spraying. Initial isolation utilized dilution and plating methods, followed by separation and purification through the streak plate technique. BLAST analysis revealed the strain's highest similarity to Deinococcus arenae SA1, with 100% homology after removing excess sequences. Subsequently, the degradation efficiency of this bacterium on paclobutrazol was evaluated by gas chromatography. Results: Quantification using the external standard method yielded a standard curve equation of y=0.0977x-0.412, with a correlation coefficient (R²) of 0.99842. Testing at different time showed that the Deinococcus arenae achieved a degradation rate of 2.49% after three days of degrading paclobutrazol. After five days, the degradation rate increased to 17.58%, reaching 38.66% after seven days, 42.20% after nine days, and 43.87% after eleven days. Conclusion: The Deinococcus arenae strain exhibited a significant degradation effect on paclobutrazol. This finding suggests potential for developing microbial agents to degrade paclobutrazol, promoting sustainable practices in agriculture.